How to update Partial Value in Postgresql?

For this particular case, the simplest way is to execute two queries.

update table set data=replace(data,'Data-','D-') where position('Data-' in data) > 0;

and

update table set data=replace(data,'INT-','I-') where position('INT-' in data) > 0;   

If the string always contain just one dash, you could do this with split_part():

update mytable set value = 
    left(value, 1) || '-' || split_part(value, '-', 2)

if there may be more than one dash, and you want everything after the first:

update mytable set value = 
    left(value, 1) || substr(value, position('-' in value))

Demo on DB Fiddle

You can use regexp_replace(). To see the new values:

select regexp_replace(value, '^(.).*(-.*)$', '\1\2')
from t;

You can interpret this as:

• ^ from the beginning of the string
• (.) take the first character and remember it.
• .* ignore any number of characters (until the following patter)
• (-.*) remember the hyphen and what follows
• $ to the end of the string

The '\1\2' is the replacement, which is the first character and then the hyphen and everything afterwards.

To change them:

update t
    set value = regexp_replace(value, '^(.).*(-.*)$', '\1\2');

Regular expressions are quite powerful. If you need to tweak the pattern matching rules, it is usually much simpler to adjust a regular expression than to deal with more cumbersome string operations.

Here is a db<>fiddle.