There doesn’t seem to be much hope of our beating that team.

意思是： 我们击败那个队的希望似乎很渺茫.
分解来看： There doesn't seem to be much hope（没有什么希望） + of our beating that team （击败那个队）
of 『 beating that team』 是一个动名词短语.动名词短语是doing+名词或代词构成的.比如 1:Thank you for『 having us』
2:『 Going to public concerts』is often free of charge.
seem 接在 does not 后面,所以用动词原形.