I've been stuck with Ampea for quite a while so I wondered if it was random like with trade contracts or if it is story and/or upgrade based?

I think it is like trade contracts, in that it appears to be random. It seems like it's also gated by story based on the fact that whenever I finish a story mission, for a while I consistently get new trade contracts or compounds - but that could have just been coincidence.

I think I stopped using the body enhancement clinic thing almost as soon as I got it - was also stuck with Ampea - and almost forgot about it for what seemed like ages. Then the following three missions/sigint each rewarded me with a new compound.

Awesome. Just me being slow then.

I've made my cabal into a little illegal weapons factory. XD

Yeah I got distracted for a while just doing every mission that popped up - since the story missions don't tend to have time limits, any other mission took priority. Eventually I just forced myself to go and do the story missions because otherwise I could easily see all of my agents becoming ridiculously overpowered.

Mine became that after the first few missions when I got supressors and two agents with Actor. XD

Compounds, as trade contacts or workshop blueprints, are randomly unlocked when you discover secret documents, finish an analytic or interrogate an agent. However, the pool of available elements is small at the beginning of the game. When you advance in the main story, more items are added to the pool and can be unlocked.

What are trade contacts? I'm pretty sure I got one a mission or so back but I don't think I ever really figured out what it was.

Does it require a new base building?

Trade contacts means you can buy that element. Select that item type in inventory and choose the buy/sell tab. You can sell anything but you will only be able to buy things you have the trade contact. No base upgrade needed.