Health centre welcomes that woman, a climbing expert? (6)
I believe the answer is:
sherpa
'a climbing expert?' is the definition.
(term for a mountain guide)
'health centre welcomes that woman' is the wordplay.
'health centre' becomes 'spa' (synonyms).
'welcomes' indicates putting letters inside (in sense of 'invites in').
'that woman' becomes 'her' (her refers to a woman).
'spa' going around 'her' is 'SHERPA'.
(Other definitions for sherpa that I've seen before include "Phrase for a native Himalayan climber" , "Skilled mountaineer of the Himalayas" , "Skilled Himalayan mountaineer" , "Phrase for Himalayan mountain climber" , "Himalayan dweller" .)