The Gosport Park outfit started the campaign with a 15-12 victory against Winchester last weekend.
After two seasons of struggling in London One south – which resulted in relegation last term – the win made a welcomed change.
Coach Simon Pickett is hoping his side can improve on that performance after grinding out a hard-earned success.
He said ‘We have not been used to winning many games so it was important we made a positive start.
‘The first game was more about the result than the performance.
‘Having got the win, it gets a losing monkey off our back right from the start.
‘When a team loses on a regular basis then it can become a little bit demoralising.
‘Beating Winchester will give everyone at the club a boost.
‘We didn’t play particularly well and know that we will need to improve a lot.’
Pickett is optimistic Gosport will have far more success this season after their opening-day win.
A number of experienced players, including brothers Wes and Wayne Dugan, and Tim Snowdon are still at the club while a couple of other influential figures have returned.
In the forwards Ben Madigan and in the three-quarters Sam Foster have both re-signed.
Hooker Sean Shepherd has moved back to Gosport Park after spending last season with Chichester.
Navy recruit Declan Gillett is a useful addition given his versatility, although he’s out injured for the next couple of weeks.
Pickett also has a number of youngsters at his disposal and he believes his veterans can help nurture the fledgling talents and ensure they reach their potential.
Wing-forward Ethan Carpenter registering an eye-catching performance against Winchester.
Pickett is expecting another tough game against Eastleigh, who started the campaign with a 9-3 win against Effingham & Leatherhead.
The Gosport coach is aware their Hampshire rivals have a strong pack of forwards that will test his troops.
‘We showed against Winchester we have the quality to grind out a win in difficult circumstances,’ Pickett added.
‘Our scrummage creaked a bit at times and we are working to strengthen our set-piece game.
‘We will need to front up against Eastleigh if we are to provide a platform to play our expansive rugby.
‘After our win last week, we can go into the game with more confidence.’
Gosport & Fareham: Penfold, Cleary, Dugan Wayne, Foster, Durrington, Dunscombe, Dugan Wes, Gamblin, Shepherd, O’Donoghue, Woodford, Roberts, Snowdon, Trevett, Madigan
Replacements: Titchenor, Bristow, Hollings