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You can just multiply the transform. Example, lets call:

oTb ( transform between odom and base_footprint, odom is the parent.)

bTf ( transform between base_footprint and frame, base_footprint is the parent.)

oTf ( transform between odom and frame, odom is the parent.)

frame here is the target_pose

oTf = oTb * bTf

So, you get this transform and simple multiply then and you have your result, the tf package and Transform class natively support this operation.