I just installed ZP on my server online..

Warning!
Your Database user must have Alter, Create, Delete, Drop, Index, Insert, Select and Update rights.

Grants found:

GRANT USAGE ON *.* TO 'xxx'@'%' IDENTIFIED BY PASSWORD 'xxx'

My host displays me only following database user permissions:
Select Update Create Insert Delete Drop

I could complete the install but would like to know if I should expect any problems?

Since you can complete the installation (I presume successfully) this is then an issue of what the Database will report to an application.

But it is also possible that you do not have `Alter` rights. In this case an upgrade to a newer version of Zenphoto might fail, depending on if the newer version has changed the database. It would be good to ask your host on this.