“Oxford learners Dictionary” states that “relief” (at least when it means removal of anxiety/pain) is an uncountable noun. Then why do we use the indefinite article in this phrase? Are there any other phrases where “relief” requires an article?
"Relief" can mean the end of pain or discomfort (uncountable), or the thing that brought about that end (countable). It's used both ways.
The full Oxford Dictionaries entry includes the countable-noun meaning of 'relief':
1.1 count noun
A cause of or occasion for relief.
‘it was a relief to find somewhere to stay’
Its use with an article is shown, but not explained, in the Oxford Learner's Dictionary:
News of their safety came as a great relief.
It was a relief to be able to talk to someone about it.
What a relief!