What is the expression for the process of getting over the loss of a loved person?
You could consider using come to terms with which means:
to start to accept and deal with a difficult situation: 'She's never really come to terms with her son's death'.
[Cambridge Idioms Dictionary, 2nd ed]
To accept could be another choice:
Tolerate or submit to (something unpleasant or undesired).
If you read the linked 5 Stages of Loss and Grief, acceptance is the last stage of Loss and Grief:
Reaching this stage of mourning is a gift not afforded to everyone. Death may be sudden and unexpected or we may never see beyond our anger or denial. It is not necessarily a mark of bravery to resist the inevitable and to deny ourselves the opportunity to make our peace. This phase is marked by withdrawal and calm. This is not a period of happiness and must be distinguished from depression.
[PsychCentral.com]
Surprised I haven't seen this, as it's the first one I think of:
Bereavement
- a period of mourning after a loss, especially after the death of a loved one:
The widow had many visitors during her bereavement.
- a state of intense grief, as after the loss of a loved one; desolation.
- deprivation or loss by force (usually fol. by of):
The hurricane left a trail of bereavement of ordinary people.