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Abstract We will use the covariant superform approach to develop a new density formula for N $$ \mathcal{N} $$ = 2 conformal supergravity which is based on a fermionic multiplet whose lowest component is a dimension-5/2 spinor. We will show that this density formula admits an embedding of the real scalar multiplet of [1]. Upon using the embedding of the tensor multiplet into the real scalar multiplet, we will construct a new higher derivative action of the tensor multiplet in N $$ \mathcal{N} $$ = 2 conformal supergravity.