The writer supports peaceful ... engrossing ... good time in national park (9)
I believe the answer is:
serengeti
'time in national park' is the definition.
'serengeti' can be an answer for 'park' (Tanzanian national park). I'm unsure of the 'time in national' bit.
'the writer supports peaceful engrossing good' is the wordplay.
'the writer' becomes 'ti' (I can't explain this - if you can you should believe this answer much more).
'supports' says to put letters next to each other (bottom letters provide a support for the top ones).
'peaceful' becomes 'serene' (similar in meaning).
'engrossing' indicates putting letters inside.
'good' becomes 'g' (abbreviation).
'serene' going around 'g' is 'serenge'.
'ti' put after 'serenge' is 'SERENGETI'.
Can you help me to learn more?
(Other definitions for serengeti that I've seen before include "Tanzanian wildlife area" , "area of the plain" , "Tanzanian plain renowned for its wildlife" , "Green ties (anag.)" , "Afr. plain; green site (anag.)" .)