Linked Field Not showing all fields

You need to set the values for the linked record field manually (or with automations or scripting). Then the values for the corresponding lookup fields will be populated automatically.

@kuovonne 
I have already added lookup fields but some of the fields are not linked and not showing values from linked records.
So is there any way to automate it so I don't have to add 1000 records manually?

This new screen shot shows values for the linked record field and the lookup fields. Some records do not have linked records, and their lookup fields are blank because those records do not have linked records. Other records have linked records, but a linked record field is blank—This typically means that either the linked records do not have a value for the field that is being looked up, or the lookup has a condition that is filtering out values. 

@kuovonne 
I don't see any condition in the lookup field or the linked fields also.
And all records - Beta Uni, Uni Country & State has values in all fields in the other table.
I don't see any blank field in the source table.

It seems like you have empty links where values contain comma (or &).
That's because if you try to fill linked field by copying values, for each value it trying to find first match, and links to it. If nothing found, it creates new empty record with that value and links to it.
That's very important to understand, to avoid wasting tables with strange empty records.
So, if you try to paste value with comma, AT process it as two values, different from value you are trying to link. In other case, it would create new records, but here it can't because it's a synced table.

Workaround? I usually create temporary duplicate field, susbstitute comma with underscore, in both tables, link table by copy-pasting field, revert _ back to ,  and remove unnecessary fields. 
But in general, I'm planning my base in a way to avoid such issues.

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@Raj wrote:

And all records - Beta Uni, Uni Country & State has values in all fields in the other table.
I don't see any blank field in the source table.

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According to you screen shot, it looks like the universities in Bolivia don't have a state in their linked table.

As for why some universities aren't linked, if you tried to fill the linked record field via copy/paste, the issue is probably as Alexey described. But the issue isn't limited to commas in the name. Quotes and some other characters can also cause the same issue. Another possibility is that the names don't match exactly--for example there might be a hidden space somewhere in one of the names.

There are various ways to fill the values, but they all depend on your actual workflow. For example, if you link via automation, you could do a "Find records" action. You could also set links via scripting.