You'll have to change your mortgage for the property that you want to rent out and then get another mortgage for the new place. But I would imagine that you may not be able to get a Buy-to-let mortgage for a shared-ownership property.
You may not be able to rent out a property if you don't own it 100%, but that will depend on your shared equity deal.
A lot of shared ownership deals have limits on things like modifications, selling, etc.
You'll also have to make sure you can afford to have the house empty and pay 2 mortgages if you don't find a tenant straight away.
The big problem I have personally with buy to let, is that a lot of people getting into the buy to let market buy up the cheaper properties pushing up the prices making it tricky for people to get onto the property ladder.
If the only way you could get onto the property ladder yourself was by using a shared equity deal, do you really think it's right to a) take up a property that was bought as shared ownership and b) take a cheaper property off the market stopping someone else who's trying to get onto the property ladder buying it (imagine that was you a couple of years ago?)
(^This is my personal opinion as someone at the bottom of the ladder, not intending to offend)
A better use for your money would be to buy out another 25% of your current place so that you "own" 75% of it. Then in another couple of years get the last 25% so you "own" all of it.
Or if you can afford the bigger mortgage, sell your current place, use the money from that as deposit on a bigger place and get yourself a mortgage for the full amount.