Mysterious Lost Cat: Timid, Gentle & Seeking Home

Black and white long hair cat, may be female, looks to be older, no microchip. Found in Cheltenham, SA. Very timid, easily frightened and gentle. This cat appeared in my yard a few months ago at first sporadically then more regularly. The cat was frightened at first, she came at night time then I noticed the cat sometimes during the day hiding in bushes. She has recently allowed me to pat her more and is very gentle and looks to of been a well loved pet.