To adapt non-TAS3 IdPs to TAS3 environment, the strategy of using SAML2 Proxy IdP profile is recommended. The TAS3 SP redirects the use to a TAS3 enabled proxy IdP (aka "middle IdP"), which then offers the user a choice of actual (non-TAS3) IdP to use and plays the SAML SP role towards that IdP. When the user has been authenticated, the assertion is returned to the middle IdP, which will use information in it to mint an assertion that is returned to the TAS3 enabled SP. The TAS3 assertion SHOULD contain the attributes of the original assertion. It MAY contain the original assertion as well, if audience restriction permits this.
The Proxy IdP Profile can also used for facilitation of interoperation across trust networks. SPs in one trust network use the IdP in their home trust network, which then contacts the foreign IdP. This way only the home trust network's IdP needs to have trust relationship with the foreign IdP. This is much more scalable than each SP having to trust directly the foreing IdPs. See [LibertyInterFed] for further discussion.
The Proxy IdP Profile is described [SAML2core] section 3.4.1.5 "Proxying" (pp.54-55) and also in [SAML2iop] section 3.3.1 IdP Proxy Feature (pp.11-12), as well as in [SAML2iopDGI] Step D (p.17-19) associated with "IdP Extended" and "SP Extended" conformance modes.