The 26-year-old midfielder has won 21 caps for his country but has not featured since he seriously injured his knee in a World Cup qualifier against Kazakhstan in October last year.
With the amount of teams featuring in the European Championships rising from 16 to 24 ahead of the 2016 event in France, Ireland are expected to feature at the tournament.
And Gibson wants to cement his place in the heart of midfield while he has the chance, starting at the Aviva Stadium this week.
"Being out for 10 months last season gave me a lot of time to think about things, and I think this is now or never, really, to be honest with you, so I am looking forward to the task ahead," Gibson said on Tuesday.
"It just made me realise that I'm not getting any younger. I need to start playing games and I need to start doing well for myself. It's a big opportunity for me."
The Everton midfielder will hope a strong performance puts him in Martin O'Neill's starting line-up for their first Euro 2016 qualifier in Georgia on Sunday.
O'Neill was delighted to welcome Gibson back to the squad and said the former Manchester United man is in good health.
He does not expect Gibson - who is yet to feature for Everton this season - to play the full game against Oman, though, as his comeback continues to be monitored.
"He's obviously a very, very decent footballer," O'Neill said.
"He hasn't played that much, but he's a very, very talented player. He looks comfortable, he looks in really decent shape. I am actually looking forward to seeing him play.
"Whether he thinks half of a game or something like that is enough for him, I don't know - most players always feel they are properly fit and fine.
"These are the sort of decisions that the two of us will consider, maybe not just necessarily for this game, but for the tournament ahead."
