Grow in your appreciation for many different styles of music. Styles like country and R&B were not things that I naturally gravitated towards in high school and college, but in the interest of trying to make myself a more well-rounded guitarist, I sought out a country guitar teacher, purchased Country and R&B albums, and focused in on what the guitar players were doing on those albums. One of the most beneficial things you can do to grow as a player try to emulate what guitarists are doing in different styles. Although guitar lessons were a big part of my learning as a player, equally important was the process of listening to a lot of stuff and copying it. This develops your ears and gets you thinking more like a musician/arranger than just a guitar player.
Play as much as you can with good musicians. There's something to be said for 'woodshedding' by yourself in your own practice space, but there's just no substitute for playing with other people. This is where you develop a few different important things. Learning to listen to what's going on in the rest of the band so that what you play complements and doesn't compete with everyone else or the vocalist. Often times in a session, I'll just sit and listen through a song a few times before I even touch my strings. I want to know, what is the mood/vibe of the song? What is the style of the song? What is the message of the song? These are all important questions to ask before you just start noodling around on the guitar. Again, this gets you thinking more like a musician and less like just a guitar player.
Invest in different pieces of gear. No serious studio guitarist has just one guitar and one amp. Most have dozens of guitars, at least a half a dozen amps, and a wide variety of effects pedals to pull from. Can great music be made with just one guitar and amp? Absolutely. But when we're talking about being a serious session player, particularly an electric guitarist, you've got to be able to get a lot of different tones. Some of that comes from your fingers, but the gear matters, too. The electric guitar, probably like no other instrument in the band, has the exciting and difficult job of creating interesting sounds and textures that can give very different vibes to different songs. The same two notes, based on what effects you're playing them through, can set a completely different mood. I always tell people to start slow with your purchases. Experiment with different amps to see what they really sound like. Try different pedals and guitars and find their nuances. Look at what bands of the past have used for gear and then listen to their albums. Part of becoming a serious studio electric guitarist is getting a 'tone education'. Yes, it can be expensive, but you can build your gear list slowly. Buy good used stuff when possible, so that if you don't love it later on, hopefully you can sell it and not lose money.
Finally, work on playing counter-melodies. A lot of playing electric guitar is the stuff in-between all-out soloing and just chord playing. Think of an amazing symphony where instruments are playing different counter-melodies over each other. I try to think like that as a guitarist, only on a smaller scale. If everyone in the band is just playing the chord changes with each other, the music will start to sound very mechanical and robotic. Look for melodic hooks and riffs that give the listener something more than chords to listen to. But make you're your counter-melodies don't fight with the main vocal melodies – another important reason to listen to what's going on around you and not just play as a soloist. It's helpful to buy a loop sampler pedal so you can record different chord changes and then work on coming up with "parts" over them. It can be a very helpful tool for coming up with different counter-melodic parts, and unless you have a good friend who can comp G, C, and D for you for hours on end, a loop sampler pedal is worth having.
