You can give discounted tickets as a gift if the discount applies to the person using the ticket. Please note that many discounts, concessions and offers are subject to proof of ID at the venue.
For example, you could give student concession tickets as a gift to a person who is a student, however you could not buy a student rate ticket and give it to someone who is not a student. They could be asked to pay full price at the venue or be refused entry, so please double check before you book.
In the case of general promotional offers, such as January Sales or Black Friday deals for example, these can be gifted to anyone to use as they are applicable for anyone to use.
You may also be interested to read Can I give Access Membership tickets as a gift?