"I did not run recently."
Translation:Níor rith mé le déanaí.
Abair is an irregular verb. The rule for irregular verbs is that irregular verbs are irregular - they don't have to follow the rules that apply to regular verbs.
The rule for the past tense is that you use níor as the negative particle. Some irregular verbs follow that rule, some don't (because they're irregular).
Both the English past tense and the English present perfect are translated into the Irish past tense , so "I have not run recently" would also be Níor rith mé le déanaí in Irish.
The English present perfect can also be translated using tar éis in certain circumstances (tá sé tar éis an rás a bhuachan), but I don't think you would use that in this case.