How would you deal with this work situation?

I work in a small team of two (myself and one other) and we have been asked by our Team Leader to look at ways of making the process easier as regards our work. I can think of a few different changes we could make but I know my colleague (who has been doing the job for the last 7 years)would not agree.

I did make her aware of what I thought would help but not wanting to ‘step on her toes’ it’s made me anxious to not take it any further. The system currently is a little ‘old’ and whilst it worked 7 years ago I feel it doesn’t now due to time, etc.

What do you think?