Английский словарь американских идиом - edge in (on)

{v. phr.} 1. To gradually approach an individual or a group with the intent of taking over or wielding power. * /Jack was edging in on the firm of Smith and Brown and after half a year actually became its vice president./ 2. To approach for capture (said of a group). * /The hunters were edging in on the wounded leopard./