The scrum half joins Abingdon School as director of rugby in September and will also be teaching PE and biology.
With school matches taking place on Saturday afternoons, Brennan will be committed to touchline duties.
This year marked the tenth anniversary of Steve Hill's appointment as Oxford University's first director of rugby.
Since then his Dark Blues side have enjoyed mixed success in the Varsity Match with a record that reads played 11, won four, lost six and drawn one.
Last week's match will have been particularly frustrating for Hill and his team after a series of impressive displays in the build-up.
To their credit, Oxford persisted with playing expansive rugby, but, on the day, they made too many errors to puncture a well-organised Cambridge defence.
As for my pre-match prediction, the less said the better!
I ended up calling the wrong winner and being 19 points out with the score.
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