Brennan is a foul-mouthed, lecherous, hypocritical and sometimes violent narcissistic bishop, who frequently abuses his power. He despises Ted, Dougal and Jack mainly because of the problems they have caused, such as Ted stealing charity money and losing it all to gambling, Dougal causing an incident that damaged several nuns and Jack with his obvious alcoholism, violence and horrible attitude, which caused a disastrous wedding. He also refers three of them as the three stooges and the cast of police academy, but he explicitly refers Dougal as cabbage.
He is greatly feared by Ted, but not so much by dim-witted Dougal while Jack views him with contempt, apologising to him with a huge amount of sarcasm after telling the Bishop to "feck off." Despite this, he ocassionally shows concern for Ted, on the occasions where Ted injures himself by jumping down the stairs and out of the window respectively, he asks if he is alright and if Ted is in need of an ambulance.
- He has a massive fear of rabbits which stems from him being trapped in a lift with them
- He also has a young son with an unnamed young woman but they live in America
- It is revealed that the reason why Jack greatly hates Brennan is because he was chosen to be a Bishop, instead of Jack. This is also one of the factor, beside his exile that causes Jack to descend into extreme alcoholism.