Fussy one-time desire to tour Arab state (3-8)
I believe the answer is:
old-womanish
'fussy' is the definition.
(I've seen this before)
'one-time desire to tour arab state' is the wordplay.
'one-time' becomes 'old'.
'desire' becomes 'wish' (wish is a kind of desire).
'to tour' means one lot of letters goes inside another (to tour can mean to go around).
'arab state' becomes 'Oman' (Oman is a Middle Eastern country).
'wish' going around 'oman' is 'womanish'.
'old'+'womanish'='OLD-WOMANISH'
(Another definition for old-womanish that I've seen is " Fussy (colloq.)".)