A Primary Key is unique by definition; that's just what the word "key" means here. So your question really becomes "do I need a Primary Key, and how would I add one?"
To answer that, you need to learn about "database normalisation", which is a set of rules for structuring data to ensure that each "fact" is stored only once. One of the key ideas in those rules is identifying which columns are "dependent" on which other columns.
For instance, in your Clients table, you presumably have data that is different between different rows for the same CustomerId (aside: shouldn't that be ClientId?) but which can be distinguished in some way. Those columns depend on both the CustomerId and some other column (version? date?), so the natural Primary Key is the combination of those two columns. A Primary Key with multiple columns is perfectly valid, but can be unwieldy to work with, so it's common in practice to add a "surrogate key", which is an arbitrary ID for every row in the table.
Where normalisation comes in is that you might also have columns that are always the same for the same CustomerId - maybe you have the date they first signed up, for instance. It wouldn't make sense to have multiple sign-up dates for the same client, so that column would depend only on the CustomerId column. Normalisation rules tell you that that belongs in a table where CustomerId is a unique column.
As you'll notice, normalisation is not something you can do one table at a time - it affects how you name things, and what columns you create - so you need to broaden your scope and plan out the data you need to store.