Fetching details from the dictionary...

upper part
upper stream; upper course of a river
skillful (in comparisons); dexterity
right side of the stage (audience's or camera's POV); stage left (actor's POV)
over-arm grip on opponent's belt
「上手」 has another reading with different meanings.
あの人は交渉で常にうわてを取る。
That person always has the upper hand in negotiations.
相手より上手でした。
I was better than my opponent.
力ではうわてだが技術では負けている。
I have the upper hand in strength but lose in technique.