Query to check if trigger exist on a MYSQL table

The accepted answer is correct and the most straightforward method, but for an enhanced view of the triggers on a table and more control over what is returned, use INFORMATION_SCHEMA:

select * from INFORMATION_SCHEMA.TRIGGERS where EVENT_OBJECT_TABLE='client';

With this, you can filter on things like EVENT_OBJECT_TABLE (table name), TRIGGER_SCHEMA, EVENT_MANIPULATION (insert, update, delete, etc), and a slew of other attributes.

As pointed out in the comments above, you'll need to have TRIGGER permissions for this method as well.

SHOW TRIGGERS

SHOW TRIGGERS LIKE '<tablename>'

e.g.

SHOW TRIGGERS LIKE 'client'