So I’m a senior service designer in government and have worked in multiple design disciplines across several departments. I have not worked in, or hired people in, graphic design so I can’t promise my advice will be entirely relevant to that. But I’ve actually signed up to MN to reply to this post (I normally just lurk) to give you some advice. And it’s possible you’re applying for one of the other disciplines (you haven’t said).
A few tips for you.
Search online for ‘Government Digital and Data Profession Capability Framework’ and read the profile for the role and level you are applying for (for example, senior graphic designer) to get an idea of the kind of skills you will be expected to demonstrate at the level you’re applying to.
I obviously don’t know which role you’re going for but generally I expect you’d need to talk about things like using and contributing to common design patterns and systems, making sure designs meet user needs and are accessible for everyone, working with others in multidisciplinary teams, reducing complexity, using data and evidence, and working with stakeholders to increase their design literacy and get buy-in for ideas etc.
You should also search for and read the following:
Government design principles
Service Manual
Design in government blog
For the application I assume it’s a CV, personal statement and possibly a portfolio.
In your personal statement you should give one strong example using the STAR technique for each criteria in the spec, rather than writing a general summary of all your experience. You need to say HOW you did things, not just that you did them.
It may be that you’ve just been saying ‘I’ve done lots of X and Y’ and not giving detailed examples, or that you’re not including enough about being strategic and working with others.
If a portfolio is needed you should focus on telling stories about solving problems, not just ‘look at this nice poster I designed’ or ‘we did a workshop with post-its and made some personas and then everything was magically better’. What problem were you solving? How did you know it was the right problem? How did you get to your solution? What challenges or compromises were involved?
A previous poster mentioned the civil service behaviours. The job advert will say what’s being tested, including any behaviours. For design roles, it’s more common for behaviours to be tested at interview not in your written application (the advert will say what is being tested at application and at interview). If behaviours are included you do really need to be aware of them as they affect the kind of answer you need to give. For example as a service designer I’ve been asked questions about user journey mapping for the behaviour Working Together (so I needed to focus on how I worked with others) and for Seeing the Big Picture (so it was more about using mapping as a way to understand and express wider context).
This isn’t meant to catch you out. Any technical skills and behaviours being tested will be listed in the job advert so you can read up and be prepared to answer questions about them. Make sure you save a copy of the job advert so you know what to prepare - often you can get to this later through the application platform but not always, so don’t risk it.
There are very few G7 roles around right now so there’s a lot of competition for roles. Are you looking up your feedback scores to see how close you are?
Anyway hope this helps. Good luck.