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In order to hear harmony, it is very helpful to see chords in their various inversions on the fretboard. Once we can visualize chords and their inversions, we can then start to stress upper structure notes within chords (13, b5, b9 #9 etc) and with practice, get those sounds locked in our heads. Then it is about locking those sounds in to our heads again and again so we grow to naturally 'hear' the relationships between individual notes when stressed against chords. In other words, once we discover the relationship between a note (say a b9 on a dominant chord) and it's underlying chord, through repetition, we can get that sound in our heads, which in turn will inspire us to improvise strong melodies.

What we need to practice is to put chords together in sequence and stress melody notes against them in a variety of ways, so we learn the relationships of chords. Let me give you an example of what I mean.

When a soloist starts to learn be-bop, his or her focus is often filling up the bars with eighth notes and 'making the changes". But are we really 'hearing' the harmony we are playing over? Let's say you have a sequence like this:

I VI II V (IE: Gmaj7, Em7, Am7, D7(b9)

A common progression. A good exercise might be to play just one note on each chord and move in an, ideally, step-wise direction either ascending or descending, at any register.

One example might be (ascending):
D, E, G, F#.

Or (descending):
D, B, C, A

Other examples:

Ascending:
F#, G, A, B
or:
A, B, C, D

Descending:
B, A, G, F#
A, G, G, F#

Of course what will really help is if we learn three inversions of each chord across the fretboard and then associate a melody note with a chord shape at the location we are at, at that time. This is a great exercise to get one used to hearing strong and weak sounds.

Another exercise, to take it a stage further, is to take a longer chord progression and practice playing one note against each chord in step-wise fashion (or as near as step-wise as possible) until the end of the sequence. Start on any string at any note (provided it is part of the chord).

And finally, really push yourself and do this on just one string. Then do the whole sequence on another string and so on. Eventually, you will start to simply 'hear' the relationships of chords and melody notes. This is a great way to instill a lyrical and melodic sense into your guitar playing.