Yes that's what I thought. He has been with other dogs all his life, one died last year so we thought we would give this a go. He loves playing with him in the garden and today I noticed the foster dog bowing his head when my dog walked in, almost to allow my dog to be the boss. Today no attacks have happened but I will be on guard and if it happens again I will reconsider the situation

Sounds like your dog is asserting his authority in the confined space of your house but when out in the open, there is less to 'guard' and both dogs have various options of action available to them hence no problems in the garden or on walks.

Good luck.

I would get a behaviourist.

What ages are the dogs? Are they entire?