Cripps was recruited by the Carlton Football Club with its first round selection in the 2013 AFL National Draft (No. 13 overall). Even as a junior, his playing style as a strong-bodied midfielder with a strong ability to win clearances by handpass drew comparisons with club great Greg Williams. Cripps made his senior debut against Melbourne in Round 4, 2014, but played only three matches during the season due to injuries. Cripps changed from his debut jumper number of 16 at the end of the 2014 season, to number 9 after it was vacated after the delisting of Kane Lucas.

In just his second season, Cripps at 195 cm/6 ft 5 in has established himself as a top inside midfielder, finishing 8th in the league for contested possessions and 11th for clearances, and earning strong acclaim for his attacking use of handball. He finished second in the 2015 AFL Rising Star award after holding favouritism with bookmakers for much of the year, and he won the John Nicholls Medal as Carlton’s best and fairest to become the second-youngest winner in the award’s history.

In 2016, Cripps further solidified his place as one the best inside midfielders in the AFL amassing 185 clearances at an average of 8.8 per game, ranked #1 in the AFL as well as 354 contested possessions at an average of 16.9, ranked #2 in the AFL for the season. After a slow start to the 2017 whilst recovering from a back injury Cripps found form to average 24.9 disposals and 6.7 clearances from 15 games before his season was cut short with a broken leg.

In October 2018, Cripps and Sam Docherty were named Carlton co-captains.