How can I make this discovered lilac tree bloom - if it is a lilac?

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I've been hacking back a mildly invasive bush that's been in the garden for decades and spread out a bit. It seems I've uncovered a neglected lilac tree that I didn't let grow of late because I just cut it back when it got too high, figuring it went with the rest of the bush. It hasn't bloomed this year - or any other in the last decade for sure - plus it's come to may attention that the new lilac trees I bought last month haven't either. Is this because they need to be settled a bit to do this? The discovered lilac hasn't had much sun, so that might be a reason it didn't bloom.

That's assuming what I've uncovered is actually a lilac? I shown a close-up of the leaves.

I'd like to give it every chance - do I need to prune part of it back? I've dug out some of the large dead wood though one is in the ground still with a leafy strand coming out of it. Does anyone have any ideas?

I don't think thats a lilac , I saw some in bloom yesterday , white and lilac together .
The leaves are a dark green almost heart shaped .

I think this is a Philadelphus/mock orange. Has sweet smelling white flowers in May. No idea when to correctly prune it.

Lilac blooms on last year's growth, you prune it immediately after flowering. I guess your new one should hopefully flower next year.

I don't think the one you've uncovered is a lilac - the leaves are the wrong shape.

If its a philadelphus you prune it after it has flowered - let it grow this year and see if it flowers next year now its getting some sun on it.

Yep agree it's probably a mock orange
I have both and my lilac is well in bloom & very heavily and the leaves are different
Our mock oranges are just starting to look like they aren't dead, blooms won't appear til later in the year - June - august

This is not lilac.

Yes, Philadelphus not lilac. Apart from leaf shape, the vein pattern is very different.

Rule of thumb with everything- prune after flowering, but if it flowers late in the year, wait till late winter

Apart from watering and feeding it, I would leave it well alone for a full year. This way you can observe it month by month. Identify any flowers that bloom and when, then look up re the care of it.

Oh I love a mock orange! My mum has a massive one at the end of the garden and you can smell it from the back door.

If you need to cut it back do it immediately after it’s flowered, then it can put on enough growth to flower next year.

This is a lilac bush. Pp are right about the heart shaped leaves, if you zoom in. Yes I did just go outside and take a pic because I am a weirdo... and partly because the party over the road is keeping me up!

It's beautiful but blooms for approx five minutes before it goes back to looking shabby and dead 🤦‍♀️

There are apps on phones now free ones that if u take a picture of the plant, tree, flower it will identify what it is. I used it when I moved into a house with a mature garden with loads of plants and trees I couldn't recognise. The app I use is called SEEK and it's free but there are better ones for a small price too.

Thanks everyone! A mock orange appears to be the consensus but it's May and no flowers to speak of. Maybe next year.
I don't know why they come by these names. The flower is white, it appears!
I may plant a white lilac - syringa limone or some such thing I've already bought - alongside it.

It’s a bit early for it to be in flower now - I have a variegated form, which is just showing buds now.

Mock orange doesn't flower till later, after the roses.

It’s called mock orange because it smells of orange blossom.

Syringa vulgaris “Madame Lemoine”?

Yes, Madame Lemoine is the one.

That's odd @NanTheWiser because I thought I'd seen a mock orange on my street today but it was in full bloom so maybe it isn't if it's not meant to have got going yet. It didn't smell of anything much which also counts against it.

Hi everyone, just posting to say that the white flowers have been out for a few weeks now! So it is verified as a monk orange - though I can't say I can detect any scent wafting from it, I have to sniff the flower to notice it. All the same, I'm very glad I uncovered this as it's now a highlight of the garden. Thanks everyone.

Oh lovely, mine, Belle Etoile, has just finished flowering, smelled divine. I'm going to cut it back this week so it has time to grow new flowering shoots for next year.

Oh, is that something I should do do mine? Its flowers have begun to wane a bit. What flowers might you put around it to match? I was going to plant the Lady of Shallot rose near it but I'm not sure the orange really goes, not sure what does go with white, really.

If you want to cut it back, now is the time to do it. But you don’t have to