[Python] How to transpose date from column to row with mapping value in python?

I have a python pandas dataframe like this:

id | Client | Type | V1 | V2 | V3 | V4 |
---------------------------------------------
0 | John | Time | 20 | 24 | | |
0 | John |Score | 7 | 8 | | |
0 | John |Level | A | B | | |
1 | Tim | Time | 15 | 19 | 20 | 18 |
1 | Tim |Score | 9 | 8 | 6 | 9 |
1 | Tim |Level | C | A | C | A |
2 | Daniel | Time | 17 | | | |
2 | Daniel |Score | 7 | | | |
2 | Daniel |Level | B | | | |​

I would like to transpose into this table:

Client | Time |Score | Level
--------------------------------
John | 20 | 7 | A |
John | 24 | 8 | B |
Tim | 15 | 9 | C |
Tim | 19 | 8 | A |
Tim | 20 | 6 | C |
Tim | 18 | 9 | A |
Daniel | 17 | 7 | B |


I read some posts using pd.melt or df.stack but it seems my case is a bit different. Any advice is appreciated.

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