Tap on the contact's name to open their profile.
If you long-pressed, a trash bin icon will appear at the top right. Tap it.
If you opened their profile, tap the three-dot menu (⋮) in the top-right corner, then select "Delete Contact".
Confirm the action by tapping "Delete" in the prompt.
Telegram might ask if you also want to delete them from telegram number database your phone's address book. Choose accordingly.
On iOS (iPhone/iPad):
Tap on the "Contacts" tab at the bottom.
Find the contact you want to delete.
Swipe left on their name and tap "Delete", or tap their name to open their profile.
If you opened their profile, tap "Edit" in the top-right corner, then scroll down and tap "Delete Contact".
Confirm by tapping "Delete Contact" again.
On Telegram Desktop:
Open the Telegram Desktop app.
Click the ☰ (three horizontal lines) menu icon in the top-left.
Select "Contacts".