Hi OP, I just ran my first half-marathon distance (i.e. 21 km) for the first time in a loooong time today. Based on that, I would say, yes!
I started like you - trying to do 10km in a reputable (sorta) time. Did that, thought, what next...... I didn't want to do a HM public event straight off, so instead I made it my NY resolution to build to a 21km run. Then, when I know I can do that distance, I can consider an event.
So I achieved my goal this morning! Possibly not the best day during a heatwave but there you are 😆
For me, I would say -
Strength training and circuits have been key. I do these anyhow, but I am convinced they have helped me build a high muscle volume that stabilises my knees and gives me strong glutes to get up hills.
Specifically, I do the standard lifts you would expect (squats etc) but I place a lot of emphasis on movements that build the glutes, unilateral like split squats and sandbag lunges, and bilateral like barbell hip thrusts. I also do a lotta press ups and I think this has built my deep core and made it easier for me to run "upright" with chest open, etc, when my body is fatiguing.
I have also started fitting in more runs in the week even "baby runs", as I think they sort of keep my legs ticking over for longer runs. That is 100% unscientific btw, but feels right to me!
Finally, and cannot emphasise this enough - yoga and foam rolling. I do yoga every single night unless I am going out for dinner or similar. Sometimes just 15 mins if that is all I have. I focus on deep stretch of the glutes and runner's lunges. Also foam roll whenever a tight spot is developing. I am convinced this helps "see off niggles" before they become actual injuries!