First-born daughter sheltering during sleet storm (6)
I believe the answer is:
eldest
'first-born' is the definition.
(the eldest child)
'daughter sheltering during sleet storm' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'sheltering during' means one lot of letters goes inside another (inserted letters are sheltered).
'storm' indicates an anagram.
'sleet' anagrammed gives 'elest'.
'd' placed within 'elest' is 'ELDEST'.
(Other definitions for eldest that I've seen before include "Most old" , "heir?" , "First in the order of birth" , "Most advanced in age, led set (anag.)" , "Most senior of two" .)