Clue: Relative cheers up over first couple of nights in country (5-5)
Answer: GREAT-NIECE
Explanation: Definition: Relative
An envelope ('in') of AT , a reversal of TA ('cheers' in the sense of "thank you"; if you are not familiar with this, keep it in mind – it pops up now and then in cryptics) plus NI ('first couple of **NI**ghts' – a construction which grates for some) in GREECE ('country').