What is the ruling on the prayer of one who has undergone surgery to extract urine from one of the kidneys via an external tube that will remain for a week?

If the discharge of urine stops for a time sufficient for ablution (wudu') and prayer, then perform ablution after the urine stops and pray.

If it is continuous, such that it does not stop for a time sufficient for both, then it falls under the ruling of سلس ( سلس البول - urinary incontinence), and it is obligatory to perform ablution for each prayer after its time has begun, and then pray. Whatever urine is discharged thereafter does not cause harm.

As for the contaminated tube, if its removal is not possible, pray with it as best as you can, and there is no need to repeat the prayer after its removal. Some scholars have said that repeating the prayer is closer to caution (ihtiyat). It is not permissible to stop praying.