From Longman Dictionary of Contemporary Englishat your earliest convenienceat your earliest convenienceformalTCMSOON as soon as possible – used in letters We should be grateful if you would reply at your earliest convenience. → convenience
Examples from the Corpus
at your earliest convenience• Could you therefore please telephone me at your earliest convenience?• We should be grateful if you would reply at your earliest convenience.• I also enclose a Medical Assessment Card which you should complete and return at your earliest convenience. 