Law helped the Ibrox club romp to a stunning 6-0 triumph over the Diamonds in the SPFL League One back in August.
But since that result - the Gers' biggest away win of the 2013/14 campaign - the Lanarkshire club have changed their manager, with Gary Bollan taking charge.
And Airdrie's form has vastly improved under the former Light Blues midfielder - they have won and drawn their last two matches.
Law, who took his tally for the season to seven with a strike in the 4-0 win over Dunfermline on Monday, said: "We had two tough games against Airdrie at Ibrox under their new manager. He had them well organised and they were difficult to break down.
"In both of those games we went in 0-0 at half-time. So we should expect another tough game. It is also difficult going to play on Astroturf too.
"They have had some great results recently and are very much an improved side. We will have to be at our best to get the victory and another three points."
Law, who netted in that 6-0 win over Airdrie at the start of the season, believes the youngsters who have come into the Rangers side have given them a lift.
Teenage winger Fraser Aird was outstanding at East End Park on Monday night - he scored the opening goal of the game and was named man of the match.
Law said: "These young lads are pushing the older boys all of the time.
"Fraser Aird has come in over the last few weeks and has taken his opportunity really well. He has been a real bright spark for us. He has made things happen with his direct running and we were all delighted when he got his goal. He got the ball rolling for us.
"I think the 1-1 draw against Stranraer in the Boxing Day game was maybe down to a lack of concentration. We maybe allowed a bit of complacency to creep into our play. But having a young lad like Fraser come in has helped us enormously. He is so enthusiastic. The manager wanted a response against Dunfermline and he got it.
"We were hurt after the Stranraer performance. We were poor and we knew it. It was our worst performance of the season by far. So it was good to bounce back with a good display and win.
"There is a lot of competition for places at the club now with the young lads coming in. Hopefully we can continue to play well in the second half of the season."