Verb (5-dan, ぐ, transitive)
1. to endure; to keep out (e.g. rain); to stave off (e.g. starvation)
これでひとまず寒さはしのげるだろう。This will at least keep the cold at bay.
2. to pull through; to get over; to survive
ひとまず今晩はしのげたわけですね。So we've managed to get through tonight, for now.
3. to surpass; to outdo; to excel; to eclipse; to defy; to slight
今年の夏の暑さは、去年をはるかにしのぐ。This summer's heat far surpasses last year's.