Little pressure to mourn (4)
I believe the answer is:
weep
'mourn' is the definition.
(both can mean to cry over something)
'little pressure' is the wordplay.
'little' becomes 'wee' (similar in meaning).
'pressure' becomes 'p' (abbreviation).
'wee'+'p'='WEEP'
'to' acts as a link.
(Other definitions for weep that I've seen before include "Bawl" , "lament" , "Display sorrow" , "Seep slowly out" , "Express grief or sorrow" .)