More lens advice

Using A65 kit lens 18:135

Looking for lowish end of  high zoom lens range, but don-t know enough yet to know what to get.

I'm thinking something with roughly 3 times the pulling power of my current SAL18135.  Probably not the right lingo but what I mean is the ability to seemingly pull things closer to you.

Seems like so often I focus on something like a bird, a bit of a ways off and when I telescope down on it... I end up wishing I could bring it a good bit closer.

Sometimes on a tour of tree identification... trying to get specific kinds of trees in certain seasons for example ...I'm often trying to id trees from a distance and would really like to be able to scope down on the leaves enough to determine what they are, so as to get them into the right folder before getting my shots.