The new recruit carried well and imposed himself throughout his side's 37-32 defeat to Exeter Chiefs at the weekend, lining up alongside James Benjamin and former Wales international Andy Powell in the back row.
But despite playing a full 80 minutes on debut, the 28-year-old New Zealander is under no illusions that competition for a place in the starting line-up will be fierce.
"It's going to be a battle and nothing is a given in this game," Crosswell told the South Wales Argus.
"I've got to get out on the field when I can and give it death.
"I am excited by the challenge but there are some guys in my position that are playing some really good footie, so getting on the field is going to be the first challenge and then I need to make the most of every bit of game time that I get."
Crosswell boasts Super Rugby experience from time spent with the Highlanders, Chiefs and Hurricanes in the southern hemisphere, and he is looking to bring that nous to the GUINNESS PRO12.
"The opportunity to play in Wales popped up and it's a part of the world that plays the style of footie that I like, the nitty-gritty and tough stuff up front," he said.
"I feel that I've got something to add and have been in some successful sides in New Zealand that play some exciting footie.
"I hope I can bring some of that here."
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