There's a few comments on here that may come across to you as a bit arsey, but there isn't really any other exercise that will have the efffect of just riding hills more often to improve your climbing mate.
I am new to cycling this year, 15 stone at 6ft, so find hills a struggle, so have avoided them where possible. When I join group rides with guys off this forum I struggle, and I am usually last up a hill. Luckily they know this and wait for me. And when I depart off on a bit of tt racing I will wait up for them.

my aim for next year is to get my hill climbing improved, by dropping weight and adding more climbs to my routes when I am out over winter.