1to peep/peek (at someone or something), often through a gap or from a distance; to observe or examine covertly
窓の隙間から部屋の中をうかがった。
I peeped into the room through the gap in the window.
彼は犯人の動向をこっそりうかがっていた。
He was secretly watching the suspect's movements.
新人は先輩の仕事ぶりをうかがって学んだ。
The newcomer learned by watching how the senior worked.
2to look for/await one's chance; to watch for an opening
敵の隙をうかがって攻撃した。
He attacked while looking for a gap in the enemy's defense.
彼は昇進のチャンスをずっとうかがっている。
He has been waiting for a chance to get promoted.
プレー中は常に相手の動きをうかがっていた。
During the game he was always watching the opponent's movements for an opening.
3to guess/infer/surmise, usually in passive constructions such as 'X can be inferred/seen from Y'
彼の言葉から本心がうかがえる。
You can infer his true feelings from his words.
外部からはその事情はうかがい知れない。
That situation cannot be known/inferred from the outside.
彼女の表情から疲れがうかがわれた。
Her expression suggested that she was tired.