The most common and most likely answer to this crossword clue is the 8 letter word TANZANIA
I've seen this crossword clue in The Daily Telegraph
T
A
N
Z
A
N
I
A
More clues leading to the result TANZANIA
- Short wacky girl going round that African country
- Brown needs one inch A-Z up country
- Reportedly beats a neighbouring republic
- Volunteers covering a little land down under, a province, and an African country
- Brown toured again leaving Gabon’s capital before crossing Zulu land
- Hit leads to frenzy, unknown for minute country
Buddy explains!

The straight part
We know that "African country" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case african country = tanzania.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.