CC driver led project
Brief:

You may have connection issues.

Driving strings arranged 2S2P may work.

Drive ONE string of four at minimum acceptable brightness
Measure and advise Vstring and I string.

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Detail:


  The old driver will not light the whole string. 


You need to explain what this means.
If you means that it lights part of the string fully and part not at all then you have connection issues.  If it lights part fully and part less brightly you have ??? issues.  

IF you can drive one string of four to acceptable brightness with the desired driver at a voltage of half or less of the driver's maximum current, then you can drive two strings in series.  

If you can drive two strings in series at acceptable brightness at less than 50% of the desired driver's  max current then you can probably drive the 4 strings in 2S2P (2 parallel  strings of 2 in series) - provided that max driver wattage is not exceeded.