Adam Ashe, Stuart Hogg and Henry Pyrgos have all committed to Warriors until 2019.
However, fellow Scotland internationals Mark Bennett, Alex Dunbar, Tommy Seymour and Josh Strauss are out of contract this summer.
"It's really important," said Blair of the need to arrange new deals.
"It's difficult with the rugby contracts, you don't often get contracts longer than two years so it seems that every year there's half the squad who are pretty much out of contract. We'll be working hard to keep the guys here.
"There's a lot of money being thrown around in England and France but the product that Glasgow can give - the coaching team, the crowd that we've got, the fact that we beat Racing home and away, we're playing against the best teams in Europe and doing well - hopefully that's a big pull for the guys as well."
Dave Rennie will replace Gregor Townsend as Glasgow head coach this summer when the latter becomes Scotland head coach.
"Dave Rennie's going to have a say in what's happening here," said former Scotland and Edinburgh scrum-half Blair.
"He's watched a lot of the games from the last two or three seasons to get a handle on what players we've got here and what he likes and what he could potentially bring in."
American lock Greg Peterson, like Ashe, Hogg and Pyrgos, has signed a new deal at Scotstoun and is nearing a return to the first team following long-term injury, along with Tjiuee Uanivi, Scott Cummings and Richie Vernon.
"We're expecting to see them back in the next two or three weeks," explained Blair.
"They're taking part in all the non-contact stuff so they're progressing well.
"Pete Horne's showing good progress. He's another couple of weeks before he can step up and we'll see how he reacts to that.
"It's good timing for us. We've got some good quality players coming back. They'll be in a good place when they come back in.
"We've got some big games coming up and some big games during the Six Nations as well once the guys are away on [Scotland duty]."
Glasgow host Cardiff Blues in the Pro12 on Saturday with the Warriors, who are fifth, nine points ahead of the Welsh province.
European Champions Cup encounters with Munster and Leicester Tigers follow, with Townsend's men currently top of Pool 1.
"We're really pleased with how things have gone recently," said Blair. "We've done well to be where we are, despite having the home losses [earlier this season].
"We're in a reasonable position. We're in a better position than we were this time last year."
Meanwhile, Glasgow say Ryan Grant remains their player after Brive announced he was joining the French Top 14 side on loan.
And Blair said: "Ryan's said that's not the situation at the moment. He's training with us today, training well."
Glasgow Warriors assistant coach Mike Blair believes it is vital the Pro12 club sign up more of their squad on new contracts.