This is a difficult slam to bid.

East is close to a jump to 2♠ but the three Club losers and lack of 16 points make 1♠ sufficient in my book (it is forcing so East knows they get another bid).

West's rebid is vital and if they venture 3♣ on the strength of their Club suit then they open the door to reaching a slam

East's 4♦ is a cue bid agreeing Clubs, West's 4♥ also a cue bid.

East now knows a Slam is on and can use 4NT (Roman Key Card Blackwood) to find out which is best

West's 5♣ shows three of the 5 Key Cards (4 Aces and ♣ K) and East now knows 6NT is definitely on