TensorFunction[t, mu, nu, ...] transform into t[LorentzIndex[mu], LorentzIndex[nu], ...], i.e., it can be used as an unspecified tensorial function t.
A symmetric tensor can be obtained by TensorFunction[{t, "S"}, mu, nu, ...], and an antisymmetric one by TensorFunction[{t, "A"}, mu, nu, ...].
Overview, FCSymmetrize, FCAntiSymmetrize.
TensorFunction[t, \[Mu], \[Nu], \[Tau]]t(\mu ,\nu ,\tau )
TensorFunction[t, \[Mu], \[Nu], \[Tau]] // StandardForm
(*t[LorentzIndex[\[Mu]], LorentzIndex[\[Nu]], LorentzIndex[\[Tau]]]*)Contract[FV[p, \[Mu]] TensorFunction[t, \[Mu], \[Nu], \[Tau]]]t\left(\overline{p},\nu ,\tau \right)
Contract[FV[p, \[Mu]] TensorFunction[t, \[Mu], \[Nu], \[Tau]]] // StandardForm
(*t[Momentum[p], LorentzIndex[\[Nu]], LorentzIndex[\[Tau]]]*)TensorFunction[{f, "S"}, \[Alpha], \[Beta]]f(\alpha ,\beta )
TensorFunction[{f, "S"}, \[Beta], \[Alpha]] // StandardForm
(*f[LorentzIndex[\[Alpha]], LorentzIndex[\[Beta]]]*)Attributes[f]
ClearAttributes[f, Orderless]\{\text{Orderless}\}