Crossword Genius

I live with cross Alpine climber (4)

Ross

I believe the answer is:

ibex

'alpine climber' is the definition.
(the ibex is a mountain goat)

'i live with cross' is the wordplay.
'live' becomes 'be' (synonyms).
'with' means one lot of letters go next to another.
'cross' becomes 'x' (X is cross-shaped).
'i'+'be'+'x'='IBEX'

(Other definitions for ibex that I've seen before include "Mountain goat with curving horns" , "one used to high living" , "Pyrenean mountain goat" , "Wild goat of North Africa" , "Sure-footed type" .)

I've seen this clue in The Times.
Want a hint initially instead of a full solution? Install my app