Generically, "if business travel ..." (without the) could be a possibility...

The whole sentence seems off. Doesn't the present tense in the first clause jar with the rest? Or is that a BE/AE difference? Plus, besides the article, doesn't "trip" sound better with "book" than "business travel"? And then do you need both "already" and "in advance"?

If the business trip will not be undertaken but has already been booked, the booking must be canceled by the employee as soon as possible.

If the business trip will not be undertaken but has been booked in advance, the booking must be canceled by the employee as soon as possible.

I don't think an ENS wrote that: "...undertaken, but has already been booked in advance,..." sounds more natural IMO.

@4 uff, danke für die Korrektur, denn der Satz im OP kam mir auch so komisch vor.

Business trip ist das, was ich als Dienstreise kenne, mit travel hab ich es noch nie gehört.

Ich würd den ganzen Klimbim umstellen:

If the trip was booked in advance, but is not undertaken, employee must cancel the booking ...

Oder so. AWWDI.

I don't think 'travel' should be used as a countable* noun in the singular** (as here). I have never heard the expression 'business journey'. So, yes, I think it should be 'business trip'.

*uncountably, ok: 'Travel broadens the mind'

**And in the plural, only in the very general sense ('My Travels in Africa'), not simply as the plural of 'trip'

from reputable co.uk. sites

"So the full cost of a business journey may be more or less than the expenses ... Ian purchases a train ticket for a business journey for £87."

(a gov.uk. site)

"Your business journey has many dangers, potholes and diversions but by getting your vehicle in shape and the sat nav programmed correctly ..."

"... answer your questions and help guide you through your business journey, providing timely advice on your most pressing business concerns."

"Record the mileage of each business journey in your diary or schedule, together with the reason for the trip, multiply that by the agreed rate and add it to your ..."

"Start by working out what counts as a business journey for you. Always record your business mileage – it helps with all methods. The method ..."

 

I think "trip" just sounds a little too colloquial in some contexts.