What is the concrete arrangement in case of an employment contract with the host of the outgoing phase in a Global Fellowship? Does the employment contract with the institution of the return phase start only when the fellow actually starts the return phase?

No. The researcher should be recruited by the institution of the return phase (the European beneficiary) under an employment contract that covers the entire duration of the grant agreement, including the outgoing phase (36 months total). It is then possible for the partner hosting the outgoing phase (the Third country organisation) to sign an additional employment contract with the researcher for just those 24 months of the outgoing phase, but the main contract will be with the beneficiary in Europe. In the practice different scenarios can occur, e.g. for the time of the outgoing phase (i.e. 24 months) the institution of the return phase will provide unpaid leave to the researcher – i.e. the researcher remains employee of the institution of the return phase but receives no salary from this institution.