Durvalumab 1500mg IV (intravenous) Q3W for up to 8 cycles (21days). Then Q4W.

Gemcitabine/Cisplatin IV (Intravenous) 1000 mg/m2 plus cisplatin 25 mg/m2 on Day 1 and Day 8 of each 21-day cycle

PFS is defined as the time from randomization until radiological progression per RECIST 1.1 or death due to any cause (in the absence of progression), whichever occurs first.

ORR is defined as the proportion of participants who have a confirmed CR or confirmed PR using RECIST 1.1.

ORR is defined as the proportion of participants who have a confirmed CR or confirmed PR using RECIST 1.1.

DoR is defined as the time from the date of first documented response until the date of documented progression using RECIST 1.1 or death due to any cause (in the absence of progression), whichever occurs first.

DoR is defined as the time from the date of first documented response until the date of documented progression using RECIST 1.1 or death due to any cause (in the absence of progression), whichever occurs first.

PFS2 is defined as the time from randomization until the earliest of the progression event (following the initial progression event), after the start of the first subsequent therapy, or death from any cause, whichever occurs first.

PFS2 is defined as the time from randomization until the earliest of the progression event (following the initial progression event), after the start of the first subsequent therapy, or death from any cause, whichever occurs first.

Safety and tolerability will be evaluated by the proportion of treated patients with occurrence of AEs and SAEs as assessed by CTCAE v5.0.

Presence of ADA for rilvegostomig (confirmatory results, titres and neutralising antibodies for confirmed positive samples).

Lowest observed plasma concentration of the study drug (Ctrough) prior to next dose

Maximum observed plasma concentration of rilvegostomig

To assess drug exposure (serum concentration) of IV rilvegostomig.

Patient reported biliary tract cancer symptoms (pain) will be evaluated by the proportion of randomized patients with maintained or improved pain as assessed by the EORTC Item Library 445 and EORTC Item Library 446 (custom questionnaires that include measures of pain-in back, in stomach area, during the night; min/max values from 1-4, with higher scores indicating a worse outcome).

Patient reported GHS/QoL will be evaluated by the proportion of randomized patients with maintained or improved GHS/QoL as assessed by the EORTC Item Library 172 (custom questionnaire that includes measures of overall health and overall quality of life; min/max values from 1-7, with higher scores indicating a better outcome).