The easiest way to have an exhibition is to arrange one yourself. Many small galleries have space to hire, then you just need to hang your work, send out invites to a preview evening and enjoy yourself. It is extremely difficult to get a gallery to give you a large solo exhibition without previous exhibiting history.
I would also advise you to exhibit one or two pieces in local shows and open exhibitions to give you a feel for exhibiting and to see how your work is received,
SAA PA Sudbury, Suffolk