Does this geas work similar to the D&D geas? I'm asking because I wanted to see how much lee-way the PC has of delaying/ignoring/side-questing this issue.
I don't know how @darkbard is handling this, but I would handle it 3-fold:
1) Start a (always table-facing) Clock (10 ticks) when this happens and Tick it once right off the bat. Call it "Death's Bargain."
2) Whenever the PC is doing something that isn't actively engaged with Death's dictate, make a soft move with some framing that portends consequence for their lack of urgency (show signs of an approaching threat or reveal an unwelcome truth). If a PC-move derived complication occurs, (1) tick the clock and (2) make manifest/act upon the badness you've portended.
3) Clock ticks full and "Death Strikes Back."