to be in breathless suspense; to be extremely tense/excited (literally: gripping with sweaty hands).
昨日の試合は手に汗握る展開で、最後まで目が離せなかった。
Yesterday's match was gripping; I couldn't take my eyes off it until the end.
プレゼン中は手に汗握ってしまい、資料の紙が少し湿っていた。
During the presentation I got so nervous that my hands were sweaty and the papers were a bit damp.
サスペンス映画のクライマックスは本当に手に汗握る場面が続いた。
The climax of the suspense movie had one truly edge-of-your-seat scene after another.
観客は手に汗握りながら選手のプレーを見守った。
The spectators watched the players' performance with bated breath.