Polish shot-stopper Grabara moved to Merseyside in January 2016 from Polish second tier side Ruch Chorzow. The Reds paid £250,000 for Grabara who moved swiftly through the ranks. After featuring in the first team's pre-season tour to the US in the summer of 2018 he was on the bench for the League Cup-tie against Chelsea at Anfield on 26 September 2018. Steven Gerrard, who was his coach at Liverpool's U-18 side, was impressed with the youngster. After Grabara's error gave Maribor the lead in a UEFA Youth League game in the 2017/18 season, he bounced back and even saved a penalty. “Nine out of ten keepers would have felt sorry for themselves and probably gone missing or tried to make up for the mistake in the wrong way,” Gerrard said. “But Kamil was very calm and experienced and bailed the team out on three or four occasions, one being the penalty. I was more pleased with his reaction to the mistake and I think that shows he is a top goalie. He is coming for crosses and making them look easy, most keepers would be in trouble with those crosses but he commands his box so well."
After Grabara signed a five-year contract last December, Liverpool Under-23s' goalkeeping coach, Mark Morris, said: "Kamil has come on in leaps and bounds. He has taken to the English game like a duck to water. He is very strong in the air, he is mentally strong, his distribution has really come on and he is brave and quick in his thinking. He listens, he works so hard and it goes to show if you get your head down, keep improving and work hard then you get the rewards. We have really high hopes for him. Kamil is a confident young boy with a big presence. He deals with crosses probably better than most goalkeepers. He seems really cut out for the English game. He is so good in one-v-one situations. He generally doesn’t just dive at an opponent’s feet and he will wait, times it right and gives them nothing to hit. He is fearless in that respect and a lot of times he will put people off just by his positional play."
Grabara was on the bench for a League Cup tie against Chelsea in September 2018, and on 6 January was loaned to Danish side Aarhus for the rest of the season. He took over from Spaniard Oscar Whalley as the club's number one, appearing sixteen times for them in a season that saw them just miss out on qualification for the Europa League. Grabara appeared in the 2019 European under 21 championships and signed a new deal with Liverpool on 15 July, before being loaned to Huddersfield for the 2019/20 season. Grabara played 28 times in the Championship but sustained a serious head injury when he was knocked out during a game with Hull City on 28 January 2020. He was then unavailable for selection until the season was suspended in March due to the COVID 19 pandemic. When it resumed behind closed doors in June, all parties decided the risk of him being involved was to great and he returned to Liverpool when the deal expired at the end of that month. Grabara was loaned to Aarhus for a second time for 2020/21. He must have impressed in the Danish league as he was sold to FC Copenhagen in the summer of 2021.