Vtyjkyuk

So I notice that the spacing between nabla and f
in math mode when using mtpro2 is really wide (for me, at least). Here is the result of typing nabla f with mtpro2.

I wonder if there is a way we can adjust the symbol nabla
based on the next non-space letter, say:

1. If the next non-space letter is f, then execute kern -0.2 em f,


2. else, stay at usual.

I have been looking around, but could not find a satisfying solution. Any help
is highly appreciated.

Here's a LuaLaTeX-based solution. It sets up a Lua function called nabla_f that does most of the work, and it assigns this function to the process_input_buffer callback, making it operate on all inputs before TeX starts is usual processing.

% !TEX TS-program = lualatex
documentclassarticle
usepackagetimes,mtpro2 % text and math fonts
usepackageluacode
beginluacode
function nabla_f ( s )
 return ( s:gsub ( "\nabla%s*f" , "\nabla\mkern-4mu f" ) )
end
endluacode
directlualuatexbase.add_to_callback("process_input_buffer", nabla_f , "nablaf" )

begindocument
$nablaf$ $nabla f$ $nabla h$ $nabla k$
enddocument

Addendum: If you also want to change the amount of whitespace between partial and f, while keeping the instruction to change the distance between nabla and f, I suggest you replace

 return ( s:gsub ( "\nabla%s*f" , "\nabla\mkern-4mu f" ) )

with

 s = s:gsub ( "\nabla%s*f" , "\nabla\mkern-4mu f" ) 
 s = s:gsub ( "\partial%s*f", "\partial\mkern-4mu f" )
 return s

Of course, you can (and should) change the new instance of -4mu to whatever the optimal adjustment amount may be.