Mental health problem not initially terribly serious (8)
I believe the answer is:
neurosis
'mental health problem' is the definition.
'neurosis' can be an answer for 'problem' (I have seen 'mental problem' mean 'neurosis' so perhaps 'problem' could also mean 'neurosis'). I'm not sure about the 'mental health' bit.
'not initially terribly serious' is the wordplay.
'initially' suggests taking the first letters.
'terribly' indicates anagramming the letters.
The initial letter of 'not' is 'n'.
'serious' is an anagram of 'eurosis'.
'n'+'eurosis'='NEUROSIS'
Can you help me to learn more?
(Other definitions for neurosis that I've seen before include "Mild mental illness often involving anxiety" , "Resinous sort of mental disorder" , "Mild mental condition" , "Mild condition such as obsessive behaviour" , "Mild mental disorder - resinous (anag)" .)