As a current flatmate, you've obviously got an interest in helping to decide who moves in. You need to to ensure they fit with the vibe of the place, and you have a chance of getting on, seeing as you're going to be living together.
Your landlord will also want to make sure that the remaining flatmates are happy with whoever moves in or they could find themselves more empty rooms to fill in the very near future!
In many cases, landlords will expect you to find the replacement flatmate, or at the very least, give you a say on their shortlist of candidates, before one of them signs the contract.
However, there is no obligation for them to involve you in the process. So the best course of action (if they're not actively involving you) is to ask politely if you can meet the prospective flatmate before their tenancy is confirmed.
Of course, if it's up to you to find a replacement for one of your flatmates, SpareRoom is here to help. Place a free ad in minutes, add photos and video for free, and let the world know how great you are to live with!
More help on replacing flatmates who move out: