Sharpish means quickly — soon, without sitting around. 'We should leave sharpish' means get going in a minute, not next week. It is British, informal, and spoken. You hear it from people who want a bit of hurry but are not barking an order. It feels friendlier than immediately, a little homely, like something a parent or a colleague might say. Though actually, -ish on other words often means 'a bit' (reddish, tallish). So students guess sharpish means 'a bit sharp', and that adjective use does exist: a sharpish knife is fairly sharp. The 'quickly' sense is the one you meet in speech, and it does not mean 'somewhat sharp' at all. Americans almost never use it this way. If you are writing careful English, pick soon or quickly instead.

（英式口語）趕快、盡快