In answer to the question, it will be done on Regimental/Corps teams. At most you might get a brigade team, but there won't be any specific "TA" team, after all we are, I am assured by the Regulars, one army.
The British Army Blades represent both Regular and Territorial. There are only a couple of Territorials in the team but the more the merrier. Various Corps and Regiments also have their own team for example REME, RLC and AAC.
There is an Inter-Service and Tri Service tournament held annually, the next being 4-6 June in Sheffield. Those who do not have a Corps or Regimental team will be placed in the 'Army All Stars' including those from the Infantry, Artillery and other arms.
If you need anymore information on the matter feel free to PM me.
We have already have one RLC Territorial based in Northern Ireland who plays for both the RLC and the Army.