Alsop, 21, has made just one County Championship appearance for his county this season after a promising end to the previous summer.
The left-hander was included in the England Lions squad tour to UAE and the North v South series during the winter.
"It's great to be back in the first team and I just want to play more and more," he told BBC Radio Solent.
Alsop's impressive first full season in 2016 culminated in a maiden first-class century against Surrey in September and 1,200 runs across all formats, including a One-Day Cup average of 54.
But he struggled for runs on the winter tours and has found himself out of favour at Hampshire in 2017 behind players such as new arrival Rilee Rossouw.
"I've been disappointed with the amount of cricket I've played so far this season, but that's to be expected with the signings we've made," Alsop said.
"They're quality international players. But it's made me more hungry and motivated to get back into the side."
Alsop has featured in Hampshire's past two T20 Blast South Group matches and hopes he can help the county push towards a quarter-final place in their remaining eight games.
"I thought about a loan move but I love playing for Hampshire," he said. "Ultimately, the goal is to play for England and you can only do that by performing and doing well in first-class cricket."
Hampshire batsman Tom Alsop hopes to make up some time with a run of games in the county's T20 Blast campaign.